Lattice Boltzmann simulation of multiphase fluid flows through the total variation diminishing with artificial compression scheme

The total variation diminishing with artificial compression (TVD/AC) scheme is applied to the lattice Boltzmann multiphase model in order to introduce a new technique to solve the traditional lattice Boltzmann equation. The TVD/AC scheme gives a much higher resolution than the well-known TVD scheme to the interface in the simulation of multiphase flows. Numerical simulations also show that the new simulator is helpful in stabilizing the computation in the runs of high-density ratios. Numerical results for the coexistence curve and verification of the Laplace law both in two and three spatial dimensions are presented. The detailed dynamical behaviors of the interface over a wide range of density ratios such as the variation of interface thickness and profiles of density, the balance of pressure and interfacial stress, the distribution of spurious velocities and so on are studied. Phase separation in two- and three-dimensional systems is also demonstrated numerically.